Our church meeting place has no wi-fi (crazy, I know) and so we prepare everything before we get there. If we were to want to add a song last minute, though, we can't even add a song that was cached in "My Songs" without an internet connection.
I really hope in future versions, we'll be able to access songs that are saved locally to help with locations like ours or also times when you might go on a retreat to somewhere with spotty internet.
Jake, I encourage you to add your suggestions and feature requests to our UserVoice page here: http://proclaim.uservoice.com This way other users can upvote your suggestions or other requests they would like to see in Proclaim.